Ukrainian Mathematical Journal

, Volume 57, Issue 9, pp 1522–1534 | Cite as

On Renewal Equations Appearing in Some Problems in the Theory of Generalized Diffusion Processes

  • M. I. Portenko


We construct a Wiener process on a plane with semipermeable membrane located on a fixed circle and acting in the normal direction. The construction method takes into account the symmetry properties of both the circle and the Wiener process. For this reason, the method is reduced to the perturbation of a Bessel process by a drift coefficient that has the type of a δ-function concentrated at a point. This leads to a pair of renewal equations, using which we determine the transition probability of the radial part of the required process.


Diffusion Process Normal Direction Symmetry Property Wiener Process Construction Method 
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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • M. I. Portenko
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKyivUkraine

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